Symplectic model reduction methods for the Vlasov equation

Abstract

Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to a high-dimensional system of ordinary differential equations. Solving such systems is computationally very expensive, especially when simulations for many different values of input parameters are desired. In this work we compare several model reduction techniques and demonstrate their applicability to numerical simulations of the Vlasov equation. The necessity of symplectic model reduction algorithms is illustrated with a simple numerical experiment.

17 pages, 5 figures

References in corpus (1)

• Stochastic variational principles for the collisional Vlasov-Maxwell and Vlasov-Poisson equations

Cited by in corpus (2)

• Stochastic variational principles for the collisional Vlasov-Maxwell and Vlasov-Poisson equations
• Learning of discrete models of variational PDEs from data